Description: The value of the interval length function. (Contributed by Mario Carneiro, 16-Mar-2014)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ovolfs.1 | |
|
Assertion | ovolfsval | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovolfs.1 | |
|
2 | 1 | fveq1i | |
3 | fvco3 | |
|
4 | 2 3 | eqtrid | |
5 | ffvelrn | |
|
6 | 5 | elin2d | |
7 | 1st2nd2 | |
|
8 | 6 7 | syl | |
9 | 8 | fveq2d | |
10 | df-ov | |
|
11 | 9 10 | eqtr4di | |
12 | ovolfcl | |
|
13 | 12 | simp1d | |
14 | 13 | recnd | |
15 | 12 | simp2d | |
16 | 15 | recnd | |
17 | eqid | |
|
18 | 17 | cnmetdval | |
19 | 14 16 18 | syl2anc | |
20 | abssuble0 | |
|
21 | 12 20 | syl | |
22 | 19 21 | eqtrd | |
23 | 11 22 | eqtrd | |
24 | 4 23 | eqtrd | |